True Strain Calculator

What Is True Strain?

True strain (also called logarithmic strain) measures deformation by considering the instantaneous change in length during deformation rather than only comparing the initial and final states.

In simple terms:

• Engineering strain measures deformation using only the original length.
• True strain measures deformation continuously as the material stretches or compresses.

Because of this, true strain is more accurate for large deformations.

Simple Example

Imagine a metal rod that stretches from 100 mm to 120 mm.

• Engineering strain measures the change relative to the original length.
• True strain measures the change at each small step during stretching.

For small deformations, both values are similar. But for large deformations, true strain becomes more precise.

True Strain Formula

True strain is calculated using the natural logarithm of the ratio between final and initial length.

Formula from Length

[
\varepsilon_t = \ln\left(\frac{L}{L_0}\right)
]

Where:

• εₜ = true strain
• L₀ = original length
• L = final length
• ln = natural logarithm

Formula from Cross-Sectional Area

When deformation occurs and volume remains constant, true strain can also be calculated from area reduction.

[
\varepsilon_t = \ln\left(\frac{A_0}{A}\right)
]

Where:

• A₀ = original cross-sectional area
• A = final cross-sectional area

This approach is common in metal forming and plastic deformation analysis.

Conversion from Engineering Strain

True strain can also be calculated from engineering strain.

[
\varepsilon_t = \ln(1 + e)
]

Where:

• e = engineering strain

This conversion is useful when engineering strain values are already available from experiments.

What Is Engineering Strain?

Engineering strain is the simpler strain measurement.

Formula

[
e = \frac{L - L_0}{L_0}
]

Where:

• e = engineering strain
• L₀ = original length
• L = final length

Engineering strain works well for small deformations, but becomes less accurate when materials experience large plastic deformation.

How the True Strain Calculator Works

The calculator you are using supports three calculation methods:

1. Calculate from Lengths

Inputs:

• Original length (L₀)
• Final length (L)

Calculation:

• True strain = ln(L / L₀)
• Engineering strain = (L − L₀) / L₀

Use this method when you measure specimen length during a tensile test.

2. Calculate from Areas

Inputs:

• Original cross-sectional area (A₀)
• Final cross-sectional area (A)

Calculation:

• True strain = ln(A₀ / A)

This method assumes volume constancy:

[
A_0 L_0 = A L
]

It is commonly used in plastic deformation and metal forming analysis.

3. Convert from Engineering Strain

Input:

• Engineering strain (e)

Calculation:

• True strain = ln(1 + e)

This option is useful when experimental results already provide engineering strain values.

Deformation States Explained

The calculator also identifies the type of deformation.

Tension (Elongation)

• True strain > 0
• The material stretches or lengthens

Example: Tensile testing of steel.

Compression (Shortening)

• True strain < 0
• The material shrinks or compresses

Example: Metal forging or compression testing.

No Deformation

• True strain = 0
• The material length remains unchanged.

Example Calculation

Let’s look at a quick example.

Given

Original length:

100 mm

Final length:

120 mm

Step 1: Engineering Strain

[
e = \frac{120 - 100}{100}
]

[
e = 0.20
]

Step 2: True Strain

[
\varepsilon_t = \ln(120/100)
]

[
\varepsilon_t = 0.182
]

Notice that true strain is slightly smaller because it accounts for incremental deformation.

Why True Strain Is Important

True strain is widely used in materials science and mechanical engineering because it reflects real material behavior during deformation.

Key Advantages

More accurate for large deformation

Engineering strain becomes inaccurate when deformation grows.

Better representation of plastic deformation

True strain captures continuous changes in geometry.

Essential for stress-strain analysis

Many material models use true stress–true strain curves.

Applications of True Strain

True strain calculations are used in many engineering fields.

Material Testing

During tensile testing, engineers calculate true strain to analyze material strength and ductility.

Metal Forming

Processes like:

• Rolling
• Forging
• Extrusion
• Drawing

rely heavily on true strain measurements.

Structural Engineering

True strain helps engineers understand material behavior under heavy loads.

Research and Material Development

Scientists use true strain to study plastic deformation and microstructure changes.

Tips for Using a True Strain Calculator

Follow these tips to avoid common mistakes.

Use consistent units

Lengths must use the same units:

• mm
• cm
• inches

Avoid zero or negative inputs

Original length and area must be greater than zero.

Understand the deformation type

Positive strain indicates tension, while negative strain indicates compression.

Choose the correct method

Use:

• Length method for tensile tests
• Area method for volume-constant deformation
• Conversion method when engineering strain is known

Common Mistakes

Confusing engineering and true strain

They are related but not identical.

Ignoring volume constancy

The area method assumes volume remains constant during deformation.

Using incorrect units

Mixed units can produce incorrect results.

True Strain vs Engineering Strain

Who Uses True Strain Calculations?

True strain calculations are important for:

• Mechanical engineers
• Material scientists
• Manufacturing engineers
• Metallurgists
• Engineering students

These professionals rely on true strain calculators to quickly analyze deformation results.